Imperfect information facilitates the evolution of reciprocity

Evolution of spite versus evolution of altruism through a disbandment mechanism

Altruism and spite are costly to the actor, making their evolution unlikely without specific mechanisms. Nonetheless, both altruistic and spiteful behaviors are present in individuals, which suggests the existence of an underlying mechanism that drives their evolution. If altruistic individuals are more likely to be recipients of altruism than non-altruistic individuals, then altruism can be favored by natural selection. Similarly, if spiteful individuals are less likely to be recipients of spite than non-spiteful individuals, then spite can be favored by natural selection. Spite is altruism's evil twin, ugly sister of altruism, or a shady relative of altruism. In some mechanisms, such as repeated interactions, if altruism is favored by natural selection, then spite is also favored by natural selection. However, there has been limited investigation into whether both behaviors evolve to the same extent. In this study, we focus on the mechanism by which individuals choose to keep or stop the interaction according to the opponent's behavior. Using the evolutionary game theory, we investigate the evolution of altruism and spite under this mechanism. Our model revealed that the evolution of spite is less likely than the evolution of altruism.

Effect of the group size on the evolution of cooperation when an exit option is present

The evolution of cooperation has been one of the main topics in evolutionary biology. If cooperators maintain interaction with cooperators and halt interaction with defectors, then cooperation can pay and can be favored by natural selection. This is called an exit option. Here, not only cooperation in dyadic interactions but also cooperation in sizable groups can be observed. Rivalry is about whether usage of the benefit by one individual reduces its availability to others or not. A common good is a rivalrous good, whereas a public good is a non-rivalrous good. In this paper, by analyzing n-player prisoner's dilemma games, we examine whether the effect of the group size on cooperation is positive or negative in the context of exit option. When goods are common goods, defectors always dominate cooperators when the group size is infinitely large. Thus, the group size has only negative effects on the evolution of cooperation when goods are common goods. In contrast, when goods are public goods, an increase in group size has positive effects as well as negative effects on the evolution of cooperation. In addition, we reveal that it has both positive and negative effects on the evolution of cooperation for cooperators to tolerate some defection and hope to keep the interaction.

Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions

Evolution of cooperation by reciprocity has been studied using two-player and n-player repeated prisoner’s dilemma games. An interesting feature specific to the n-player case is that players can vary in generosity, or how many defections they tolerate in a given round of a repeated game. Reciprocators are quicker to detect defectors to withdraw further cooperation when less generous, and better at maintaining a long-term cooperation in the presence of rare defectors when more generous. A previous analysis on a stochastic evolutionary model of the n-player repeated prisoner’s dilemma has shown that the fixation probability of a single reciprocator in a population of defectors can be maximized for a moderate level of generosity. However, the analysis is limited in that it considers only tit-for-tat-type reciprocators within the conventional linear payoff assumption. Here we extend the previous study by removing these limitations and show that, if the games are repeated sufficiently many times, considering non-tit-for-tat type strategies does not alter the previous results, while the introduction of non-linear payoffs sometimes does. In particular, under certain conditions, the fixation probability is maximized for a “paradoxical” strategy, which cooperates in the presence of fewer cooperating opponents than in other situations in which it defects.

Which facilitates the evolution of cooperation more, retaliation or persistence?

The existence of cooperation in this world is a mysterious phenomenon. One of the mechanisms that explain the evolution of cooperation is repeated interaction. If interactions between the same individuals repeat and individuals cooperate conditionally, cooperation can evolve. A previous study pointed out that if individuals have persistence (i.e., imitate its "own" behavior in the last move), cooperation can evolve. However, retaliation and persistence are not mutually exclusive decisions, but rather a trade-off in the decision making process of individuals. Players can refer to the opponent's behavior and if the actor and the opponent opted for the different alternative in the last move, conditional cooperators have to give up either retaliation or persistence. The previous study also investigated this, and has revealed that the individual should give more importance to retaliation than to persistence. However, this study has assumed that the errors in perception are absent. In this world, errors in perception are present, and trying to imitate the opponent player can sometimes end in failure. And, it might be that imitating the focal player, which definitely ends in success, is more beneficial than trying to imitate the opponent player, which can end in failure especially when the error rate in recognition is large. Here, this paper uses evolutionarily stable strategy (ESS) analysis and analyzes the stability for reactive strategies against the invasion by unconditional defectors in the iterated prisoner's dilemma game. And our analysis reveals that even if we take errors in perception into consideration, retaliation facilitates the evolution of cooperation more than persistence unexpectedly. In addition, we analyze the stability for reactive cooperators against the invasion by a strategy other than unconditional defectors. Moreover, we also analyze the deterministic model in which unconditional cooperators, unconditional defectors, and the reactive strategy at the same time.

Unified and simple understanding for the evolution of conditional cooperators

Cooperation is a mysterious phenomenon which is observed in this world. The potential explanation is a repeated interaction. Cooperation is established if individuals meet the same opponent repeatedly and cooperate conditionally. Previous studies have analyzed the following four as characters of conditional cooperators mainly. (i) niceness (i.e., when a conditional cooperator meets an opponent in the first place, he (she) cooperates or defects), (ii) optimism (when a conditional cooperator meets an opponent in the past, but he (she) did not get access to information about the opponent's behavior in the previous round, he (she) cooperates or defects), (iii) generosity (even when a conditional cooperator knows that an opponent defected in the previous round, he (she) cooperates or defects) and (iv) retaliation (a conditional cooperator cooperates with a cooperator with a higher probability than with a defector). Previous works deal with these four characters mainly. However, these four characters basically have been regarded as distinct topics and unified understanding has not been done fully. Here we, by studying the iterated prisoner's dilemma game (in particular, additive games) and using evolutionarily stable strategy (ESS) analysis, find that when retaliation is large, the condition under which conditional cooperators are stable against the invasion by an unconditional defector is loose, while none of "niceness", "optimism", and "generosity" makes impact on the condition under which conditional cooperators are stable against an invasion by an unconditional defector. Furthermore, we show that we can understand "niceness", "optimism", and "generosity" uniformly by using one parameter indicating "cooperative", and when the conditional cooperators have large "retaliation" enough to resist an invasion by an unconditional defector, natural selection favors more "cooperative" conditional cooperators to invade the resident conditional cooperative strategy. Moreover, we show that these results are robust even when taking the existence of mistakes in behavior into consideration.